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Entropy

Ising Ladder with Four-Spin Plaquette Interaction in a Transverse Magnetic Field

J. A. Plascak, Maria Eugénia Nunes, F. W. S. Lima

Published Dec 16, 2023• 4 citations
Publisher

Abstract

The spin-1/2 quantum transverse Ising model, defined on a ladder structure, with nearest-neighbor and four-spin interaction on a plaquette, was studied by using exact diagonalization on finite ladders together with finite-size-scaling procedures. The quantum phase transition between the ferromagnetic and paramagnetic phases has then been obtained by extrapolating the data to the thermodynamic limit. The critical transverse field decreases as the antiferromagnetic four-spin interaction increases and reaches a multicritical point. However, the exact diagonalization approach was not able to capture the essence of the dimer phase beyond the multicritical transition.

DOI
10.3390/e25121665

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The spin-1/2 transverse field two-leg Ising ladder with nearest-neighbor exchange and plaquette four-spin interaction J4{J}_{4}J4​ is studied analytically and numerically with the density matrix renormalization group approach. The quantum phase diagram in the transverse field BBB versus J4{J}_{4}J4​ plane has been obtained. There are three different phases: a paramagnetic (PM) phase for high values of the transverse field and, for low values of BBB, a ferromagnetic (FM) ordered phase for small J4{J}_{4}J4​, and a dimerized-rung (DR) phase for large negative values of J4{J}_{4}J4​. All phases are separated by quantum phase transition lines meeting at a multicritical point. The critical lines have been obtained by exploring the entanglement entropy. The results show that along the critical lines the central charge is c=1/2c=1/2c=1/2, while at the multicritical point one has c=1c=1c=1. The scaling dimension of the energy operator is ${X}_{\ensuremath{\epsilon}}=1$, in agreement with the universality class of the critical behavior of the quantum Ising chain. An effective field theory for the multicritical point is also discussed. The FM and the DR order parameters have also been computed and we found a region where the FM and the DR phases coexist.
We apply a finite-size scaling approach to the one-dimensional spin-1/21/21/2 Ising model with nearest- and next-nearest-neighbor interactions in the presence of a transverse magnetic field. By using the scaling behavior of the energy gap we are able not only to determine the ferromagnetic-paramagnetic transition line at zero absolute temperature but also to compute the corresponding critical exponent. A comparison with other approaches is made, and aside for small discrepancies likely to occur at the thermodynamic limit, we believe that the present results are quite close to the unknown exact ones.
The critical properties of the one-dimensional spin-1/2 transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility was used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction J_{2}, we calculated the fidelity susceptibility as a function of the transverse field B_{x} and the longitudinal field B_{z}. The phase diagram in the (B_{x},B_{z})-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For B_{x}<1, we observed an antiferromagnetic phase for small values of B_{z} and a paramagnetic phase for large values of B_{z}. For B_{x}>1 and low B_{z}, we found a disordered phase that undergoes a second-order phase transition to a paramagnetic phase for large values of B_{z}.
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